Probability Colloquium Augsburg-Munich
Speakers:
Schedule:
Titles and abstracts:
Mia Deijfen: Into space – and back again!
Abstract: The configuration model is a standard model for generating a random graph with a prescribed degree distribution. I will describe attempts to analyze a spatial version of the model, and ongoing work to revert the spatial model to the non-spatial setting.
Remco van der Hofstad: The number and structure of connected graphs with a fixed degree sequence
We study connected graphs with a fixed degree sequence, in the sparse setting where the number of edges grows linearly in the number of vertices. Using the relation to the configuration model, we identify the number of such connected graphs up to a subexponential order. We do this by viewing a connected graph with a given degree distribution as the realization of the giant component in a larger configuration model, and carefully choosing the degree distribution of the larger graph so that it is likely that its giant component has the required degree distribution. To ensure that the connected graph has exactly the correct degrees, we use a switching argument. We further identify the local structure of a uniform random graph with prescribed degrees. This is joint work with Sasha Bell and Serte Donderwinkel.